Problem: Rewrite as a simplified fraction. ${0.7\overline{25} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 725.2525...\\ 10x &= 7.2525...\end{align*}}$ Subtracting the two equations, we have: ${990x = 718}$ ${x = \dfrac{718}{990}} $ ${x = \dfrac{359}{495}} $